A universal integral as common frame for choquet and sugeno integral

Erich Peter Klement, Radko Mesiar, Endre Pap

Research output: Contribution to journalArticle

216 Citations (Scopus)

Abstract

The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is restricted because of the special operations used in the construction of these integrals. Therefore, we provide a concept of integrals generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures. For a fixed pseudomultiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced, and the restriction to the unit interval, i.e., to fuzzy integrals, is considered.

Original languageEnglish
Article number5361437
Pages (from-to)178-187
Number of pages10
JournalIEEE Transactions on Fuzzy Systems
Volume18
Issue number1
DOIs
Publication statusPublished - Feb 1 2010

Keywords

  • Aggregation
  • Choquet integral
  • Pseudomultiplication
  • Sugeno integral
  • Universal integral

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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